Finite Group Databasebeta

← #11898374

Subgroups — #11898374

Order 1152.

787 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594350C212yesmaximal, complemented
2#10592571C211yesmaximal, characteristic
3C3×#4873C212yesmaximal, complemented
4#10590905C211yesmaximal, characteristic, complemented
5#10590865C212yesmaximal
6C8×#627C211yesmaximal, characteristic, complemented
7#10590565C212yesmaximal, complemented
8#10590536C214yesmaximal, complemented
9#79710—32nomaximal
10C2×#3745C2211yescharacteristic
11#64102C2212yes—
12C2×C3×Dic12C2212yes—
13C3×#887C2214yes—
14C4×#627C2211yescharacteristic
15#63874—22no—
16#63873C2212yes—
17#63868—24no—
18#63865—22no—
19#63864C2214yes—
20C2×#3718C2212yes—
21C2×#3717C2214yes—
22C32×#107C2211yescharacteristic
23C8×C3⋊Dic3C2211yescharacteristic
24#63636C2212yes—
25C3×C8×Dic3C2212yes—
26C3×#810C2214yes—
27#63572C2211yescharacteristic
28Dic3⋊(C3⋊C8)C2212yes—
29#5568—34no—
30C3×C4×Q16—32no—
31#5191—32no—
32#5183—32no—
33#5028—34no—
34#4873D312yescomplemented
35#4872—32no—
36#4872—61no—
37#4818—34no—
38#4798—34no—
39#4696—32no—
40C8×Dic6—32no—
41C2×C4⋊(C3⋊D3)C2312yes—
42C2×C4×C3⋊D3—22no—
43C2×C3×Dic6C2314yes—
44C2×#627D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46C32×C4⋊C4C2312yes—
47#3752—22no—
48C4×C3⋊Dic3C2311yescharacteristic
49C2×C3⋊(C3⋊C8)C2311yescharacteristic
50#3745—22no—
51C3×Dic3⋊C4—24no—
52C3×C4×Dic3—24no—
53C3×C4×Dic3C2312yes—
54C2×C3×C3⋊C8C2312yes—
55C3×Dic12—24no—
56#3724—22no—
57#3724—22no—
58#3724D411yescharacteristic
59Dic3⋊Dic3D412yes—
60#3722—24no—
61#3722—24no—
62#3718—42no—
63#3717—44no—
64#3393—91noSylow
65C2×C3×Q16—32no—
66C3×C4×Q8—34no—
67#947—34no—
68#944—34no—
69C2×#216—34no—
70C2×#215—34no—
71C2×Dic12C2×D312yes—
72C2×D24—32no—
73C2×D24—61no—
74C2×#204—34no—
75#898—64no—
76#896—64no—
77#893—34no—
78#893—62no—
79#887C2×D314yes—
80#876—64no—
81#875—34no—
82#872—64no—
83C4×Dic6—32no—
84C3×#107—21no—
85C3×#107C2×D312yes—
86C3×#103—34no—
87C3×C4×C8—32no—
88Dic3⋊C8—32no—
89Dic3⋊C8—32no—
90C8×Dic3—32no—
91C8×Dic3—61no—
92C8×Dic3C2×D312yes—
93#810C2×D314yes—
94#809—34no—
95#809—62no—
96C4⋊(C3⋊C8)—32no—
97C22×C3⋊D3—22no—
98C2×C32×C4—22no—
99C2×C32×C4C2411yescharacteristic
100C2×C3⋊Dic3C2×D411yescharacteristic
101C2×C3⋊Dic3C2×D411yescharacteristic
102C4⋊(C3⋊D3)—22no—
103C4⋊(C3⋊D3)—22no—
104C4×C3⋊D3—44no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3C2×D412yes—
107C2×C3×Dic3C2×D412yes—
108C3×Dic6—24no—
109C3×Dic6—24no—
110#627—22no—
111C32×C8#4112yes—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—22no—
114#556—92no—
115#495—92no—
116#494—91no—
117#464—94no—
118#461—92no—
119C8×Q8—91no—
120C4×Q16—32no—
121C4×D8—91no—
122C2×C3×Q8—34no—
123C2×D12—34no—
124C2×D12—62no—
125C2×C4×D3—64no—
126C2×C4×D3—122no—
127C2×Dic6—32no—
128C2×Dic6C22×D314yes—
129C3×Q16—64no—
130C2×C3×C8—21no—
131C2×C3×C8—32no—
132C2×C3×C8C22×D312yes—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—64no—
135C3×C4⋊C4C22×D314yes—
136C3×C42—32no—
137C3×C42—64no—
138#216—124no—
139#215—124no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142(C2×D3)⋊C4—64no—
143(C2×D3)⋊C4—64no—
144(C2×D3)⋊C4—64no—
145(C2×D3)⋊C4—122no—
146C4⋊Dic3—32no—
147Dic3⋊C4—24no—
148Dic3⋊C4—32no—
149Dic3⋊C4—32no—
150Dic3⋊C4—64no—
151Dic3⋊C4—64no—
152C4×Dic3—24no—
153C4×Dic3—32no—
154C4×Dic3—61no—
155C4×Dic3C22×D312yes—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8C22×D312yes—
159Dic12—24no—
160D24—64no—
161D24—64no—
162#204—124no—
163C22×C32C22×D411yescharacteristic
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—42no—
167C32×C4—42no—
168C32×C4C2×#4111yescharacteristic
169C32×C4H(5,𝔽2)11yescharacteristic
170C3⋊Dic3—21no—
171C3⋊Dic3#13512yes—
172C3×Dic3—22no—
173C3×Dic3—22no—
174C3×Dic3—44no—
175C2×Q16—32no—
176C2×Q16—92no—
177C2×SD16—94no—
178C2×D8—91no—
179C4⋊Q8—92no—
180#126—184no—
181#124—94no—
182C22⋊Q8—182no—
183C4×Q8—34no—
184C4×Q8—91no—
185C4×D4—92no—
186#117—182no—
187#107D3211yescharacteristic
188C4⋊C8—92no—
189C4⋊C8—91no—
190#103—34no—
191#102—92no—
192C4×C8—32no—
193C4×C8—91no—
194C22×D3—64no—
195C22×D3—122no—
196C3×Q8—64no—
197C3×Q8—64no—
198C2×C3×C4—24no—
199C2×C3×C4—21no—
200C2×C3×C4—32no—
201C2×C3×C4—32no—
202C2×C3×C4—42no—
203C2×C3×C4—64no—
204C2×C3×C4C23×D312yes—
205C2×Dic3—24no—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3D3×D412yes—
211C2×Dic3D3×D412yes—
212D12—64no—
213D12—64no—
214D12—64no—
215D12—122no—
216C4×D3—128no—
217C4×D3—244no—
218Dic6—24no—
219Dic6—24no—
220Dic6—64no—
221C3×C8—22no—
222C3×C8—62no—
223C3×C8#23514yes—
224C3⋊C8—22no—
225C3⋊C8—62no—
226C3⋊C8—121no—
227C2×C32#55011yescharacteristic
228C2×C32C2×#13511yescharacteristic
229C2×C32#57811yescharacteristic
230C3⋊D3—82no—
231C2×Q8—34no—
232C2×Q8—91no—
233C2×D4—92no—
234C22×C4—182no—
235Q16—64no—
236Q16—362no—
237SD16—364no—
238D8—182no—
239C2×C8—32no—
240C2×C8—91no—
241C2×C8C2×D3211yescharacteristic
242C4⋊C4—64no—
243C4⋊C4—91no—
244C4⋊C4—92no—
245C4⋊C4—182no—
246C4⋊C4—182no—
247C4⋊C4C2×D3212yes—
248C22⋊C4—182no—
249C22⋊C4—184no—
250C22⋊C4—184no—
251C42—32no—
252C42—64no—
253C42—91no—
254C22×C3—21no—
255C22×C3C2×D3×D412yes—
256C2×D3—124no—
257C2×D3—124no—
258C2×D3—124no—
259C2×D3—124no—
260C2×D3—242no—
261C2×D3—242no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—44no—
265C3×C4—62no—
266C3×C4—62no—
267C3×C4—82no—
268C3×C4—124no—
269C3×C4C2×#23512yes—
270C3×C4#100912yes—
271Dic3—22no—
272Dic3—22no—
273Dic3—34no—
274Dic3—44no—
275Dic3—62no—
276Dic3—62no—
277Dic3—121no—
278C32#339311yescharacteristic, complemented, Sylow
279C23—182no—
280Q8—64no—
281Q8—64no—
282Q8—182no—
283D4—182no—
284D4—182no—
285C2×C4—22no—
286C2×C4—32no—
287C2×C4—32no—
288C2×C4—64no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—364no—
292C2×C4C22×D3211yescharacteristic
293C8—62no—
294C8—181no—
295C8#379812yes—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#555312yes—
300C2×C3#576612yes—
301C2×C3D3×#13512yes—
302D3—244no—
303D3—244no—
304C22—362no—
305C22—362no—
306C22—362no—
307C22D32×D411yescharacteristic
308C4—42no—
309C4—62no—
310C4—62no—
311C4—92no—
312C4—124no—
313C4—181no—
314C4C2×#379811yescharacteristic
315C4#6432011yescharacteristic
316C3—21no—
317C3#7971012yescomplemented
318C2—722no—
319C2#1059452011yescharacteristic
320C2#1059473011yescharacteristic
321C2#1059476511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#107D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10594350C2semidirect
3. C3×#4873C2semidirect
4. #10590905C2semidirect
6. C8×#627C2semidirect
7. #10590565C2semidirect
8. #10590536C2semidirect
34. #4873D3semidirect
278. C32#3393semidirect
317. C3#79710semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105943502
#105925712
C3×#48732
#105909052
#105908652
C8×#6272
#105905652
#105905362
#797103